气溶胶对雷暴云微物理过程和起电影响的数值模拟
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摘要
将云滴冻结方案植入已有的二维雷暴云起、放电模式,结合一次山地雷暴个例,探讨了气溶胶浓度对雷暴云微物理过程、起电以及空间电荷结构的影响。结果表明:气溶胶浓度增加,云滴数目增多,尺度降低,雨滴含量减少;云滴冻结导致冰晶在低温区快速生长,冰晶数浓度增加,尺度减小,当气溶胶浓度高于1000 cm-3后小冰晶难以增长成大尺度的霰粒子,因此霰粒子数浓度先增加后急剧减少。此外,气溶胶浓度的大小不会影响雷暴云的电荷结构特征,但会对云内的起电强度产生明显的作用:当气溶胶浓度较低时,增加气溶胶浓度,更多的冰晶和霰粒子发生碰撞使得云内起电过程增强,空间电荷密度增加;当气溶胶浓度高于1000 cm-3后,少量的霰粒子和小冰晶的出现抑制了非感应起电过程,导致电荷密度降低。
A two-dimensional(2-D) cumulus model with electrification and lightning processes is implemented to investigate aerosol effects on microphysical process, electrification, and charge structure in thunderstorms. The 2-D cumulus model coupled with a droplet freezing module is used to simulate a SEET(Studies of Electrical Evolution in Thunderstorms) case. The results show that the number concentration of cloud droplets increases and its scale decreases with increasing aerosol concentration, but the content of raindrops reduces. Ice crystals grow rapidly in low temperature region, which is attributed to droplets freezing, and the number concentration of ice crystals increases but the scale decreases. The number concentration of graupels increases first and then decreases sharply because ice crystals are difficult to grow into graupels with larger scale when the aerosol concentration exceeds 1000 cm-3. In addition, the charge structure of thunderstorms is not affected by aerosol concentration, but aerosols have significant effect on the strength of electrification, i.e., when the aerosol concentration is lower, more ice crystals and graupels collision enhances the non-inductive charging process and increases the charge density as the aerosol concentration increases; however, the non-inductive charging rate starts to decrease when the aerosol concentration exceeds 1000 cm-3 due to the appearance of small ice crystals and little graupels, and the charge density is reduced.
A two-dimensional(2-D) cumulus model with electrification and lightning processes is implemented to investigate aerosol effects on microphysical process, electrification, and charge structure in thunderstorms. The 2-D cumulus model coupled with a droplet freezing module is used to simulate a SEET(Studies of Electrical Evolution in Thunderstorms) case. The results show that the number concentration of cloud droplets increases and its scale decreases with increasing aerosol concentration, but the content of raindrops reduces. Ice crystals grow rapidly in low temperature region, which is attributed to droplets freezing, and the number concentration of ice crystals increases but the scale decreases. The number concentration of graupels increases first and then decreases sharply because ice crystals are difficult to grow into graupels with larger scale when the aerosol concentration exceeds 1000 cm-3. In addition, the charge structure of thunderstorms is not affected by aerosol concentration, but aerosols have significant effect on the strength of electrification, i.e., when the aerosol concentration is lower, more ice crystals and graupels collision enhances the non-inductive charging process and increases the charge density as the aerosol concentration increases; however, the non-inductive charging rate starts to decrease when the aerosol concentration exceeds 1000 cm-3 due to the appearance of small ice crystals and little graupels, and the charge density is reduced.
引文
Coleman L M,Marshall T C,Stolzenburg M,et al.2003.Effects of charge and electrostatic potential on lightning propagation[J].J.Geophys.Res.,108(D9):4298,doi:10.1029/2002JD002718.
Cooper W A.1980.A method of detecting contact ice nuclei using filter samples[C]//Proceedings of the 8th International Conference on Cloud Physics.Clermont-Ferrand,France,665-668.
邓美玲,银燕,赵鹏国,等.2017.云凝结核浓度对雷暴云电过程影响的数值模拟研究[J].大气科学,41(1):106-120.Deng Meiling,Yin Yan,Zhao Pengguo,et al.2017.Effects of cloud condensation nuclei concentration on the electrification of thunderstorm:A numerical simulation[J].Chinese Journal of Atmospheric Sciences(in Chinese),41(1):106-120,doi:10.3878/j.issn.1006-9895.1608.15286.
Fan J W,Zhang R Y,Li G H,et al.2007.Simulations of cumulus clouds using a spectral microphysics cloud-resolving model[J].J.Geophys.Res.,112(D4):D04201,doi:10.1029/2006JD007688.
Fletcher N H.1962.Physics of Rain Clouds[M].London:Cambridge University Press,390pp.
Gardiner B,Lamb D,Pitter R L,et al.1985.Measurements of initial potential gradient and particle charges in a Montana summer thunderstorm[J].J.Geophys.Res.,90(D4):6079-6086,doi:10.1029/JD090iD04p06079.
Heymsfield A J,Miloshevich L M.1993.Homogeneous ice nucleation and supercooled liquid water in orographic wave clouds[J].J.Atmos.Sci.,50(15):2335-2353,doi:10.1175/1520-0469(1993)050<2335:HINASL>2.0.CO;2.
Heymsfield A J,Miloshevich L M,Schmitt C,et al.2005.Homogeneous ice nucleation in subtropical and tropical convection and its influence on cirrus anvil microphysics[J].J.Atmos.Sci.,62(1):41-64,doi:10.1175/JAS-3360.1.
Heymsfield A J,Sabin R M.1989.Cirrus crystal nucleation by homogeneous freezing of solution droplets[J].J.Atmos.Sci.,46(14):2252-2264,doi:10.1175/1520-0469(1989)046<2252:CCNBHF>2.0.CO;2.
胡志晋,何观芳.1987.积雨云微物理过程的数值模拟(一)微物理模式[J].气象学报,45(4):467-484.Hu Zhijin,He Guanfang.1987.Numerical simulation of microprocesses in cumulonimbus clouds(I)microphysical model[J].Acta Meteorologica Sinica(in Chinese),45(4):467-484,doi:10.11676/qxxb1987.060.
Kar S K,Liou Y A,Ha K J.2009.Aerosol effects on the enhancement of cloud-to-ground lightning over major urban areas of South Korea[J].Atmospheric Research,92(1):80-87,doi:10.1016/j.atmosres.2008.09.004.
Li G H,Wang Y,Zhang R Y.2008.Implementation of a two-moment bulk microphysics scheme to the WRF model to investigate aerosol-cloud interaction[J].J.Geophys.Res.,113(D15):D15211,doi:10.1029/2007JD009361.
Lyons W A,Uliasz M,Nelson T E.1998.Large peak current cloud-toground lightning flashes during the summer months in the contiguous United States[J].Mon.Wea.Rev.,126(8):2217-2233,doi:10.1175/1520-0493(1998)126<2217:LPCCTG>2.0.CO;2.
Mansell E R,MacGorman D R,Ziegler C L,et al.2002.Simulated three-dimensional branched lightning in a numerical thunderstorm model[J].J.Geophys.Res.,107(D9):4075,doi:10.1029/2000JD000244.
Mansell E R,MacGorman D R,Ziegler C L,et al.2005.Charge structure and lightning sensitivity in a simulated multicell thunderstorm[J].J.Geophys.Res.,110(D12):D12101,doi:10.1029/2004JD005287.
Mansell E R,Ziegler C L.2013.Aerosol effects on simulated storm electrification and precipitation in a two-moment bulk microphysics model[J].J.Atmos.Sci.,70(7):2032-2050,doi:10.1175/JAS-D-12-0264.1.
Mitzeva R,Latham J,Petrova S.2006.A comparative modeling study of the early electrical development of maritime and continental thunderstorms[J].Atmospheric Research,82(1-2):26-36,doi:10.1016/j.atmosres.2005.01.006.
Murray N D,Orville R E,Huffines G R.2000.Effect of pollution from Central American fires on cloud-to-ground lightning in May 1998[J].Geophys.Res.Lett.,27(15):2249-2252,doi:10.1029/2000GL011656.
Orville R E,Huffines G,Nielsen-Gammon J,et al.2001.Enhancement of cloud-to-ground lightning over Houston,Texas[J].Geophys.Res.Lett.,28 (13):2597-2600,doi:10.1029/2001GL012990.
Saunders C P R,Keith W D,Mitzeva R P.1991.The effect of liquid water on thunderstorm charging[J].J.Geophys.Res.,96(D6):11007-11017,doi:10.1029/91JD00970.
Shi Z,Tan Y B,Tang H Q,et al.2015.Aerosol effect on the land-ocean contrast in thunderstorm electrification and lightning frequency[J].Atmospheric Research,164-165:131-141,doi:10.1016/j.atmosres.2015.05.006.
师正,谭涌波,唐慧强,等.2015.气溶胶对雷暴云起电以及闪电发生率影响的数值模拟[J].大气科学,39(5):941-952.Shi Zheng,Tan Yongbo,Tang Huiqiang,et al.2015.A numerical study of aerosol effects on the electrification and flash rate of thunderstorms[J].Chinese Journal of Atmospheric Sciences(in Chinese),39(5):941-952,doi:10.3878/j.issn.1006-9895.1412.14230.
Steiger S M,Orville R E.2003.Cloud-to-ground lightning enhancement over Southern Louisiana[J].Geophys.Res.Lett.,30(19):1975,doi:10.1029/2003GL017923.
Sun A P,Chun H Y,Baik J J,et al.2002.Influence of electrification on microphysical and dynamical processes in a numerically simulated thunderstorm[J].J.Appl.Meteor.,41:1112-1127,doi:10.1175/1520-0450(2002)041<1112:IOEOMA>2.0.CO;2.
Takahashi T.1978.Riming electrification as a charge generation mechanism in thunderstorms[J].J.Atmos.Sci.,35(8):1536-1548,doi:10.1175/1520-0469(1978)035<1536:REAACG>2.0.CO;2.
谭涌波.2006.闪电放电与雷暴云电荷、电位分布相互关系的数值模似[D].中国科学技术大学博士学位论文,173pp.Tan Yongbo.2006.Numerical simulation of the relationship of the lightning discharge with the space charge and potential distribution in thundercloud[D].Ph.D.dissertation(in Chinese),University of Science and Technology of China,173pp.
Tan Y B,Peng L,Shi Z,et al.2016.Lightning flash density in relation to aerosol over Nanjing(China)[J].Atmospheric Research,174-175:1-8,doi:10.1016/j.atmosres.2016.01.009.
Tan Y B,Shi Z,Chen Z L,et al.2017.A numerical study of aerosol effects on electrification of thunderstorms[J].Journal of Atmospheric and SolarTerrestrial Physics,154:236-247,doi:10.1016/j.jastp.2015.11.006.
Tan Y B,Tao S C,Liang Z W,et al.2014.Numerical study on relationship between lightning types and distribution of space charge and electric potential[J].J.Geophys.Res.,119(2):1003-1014,doi:10.1002/2013JD019983.
谭涌波,马肖,向春燕,等.2017.气溶胶对雷暴云电过程影响的数值模拟研究[J].地球物理学报,60(8):3041-3050.Tan Yongbo,Ma Xiao,Xiang Chunyan,et al.2017.A numerical study of the effects of aerosol on electrification and lightning discharges during thunderstorms[J].ChineseJournal of Geophysics(in Chinese),60(8):3041-3050,doi:10.6038/cjg20170812.
谭涌波,陶善昌,祝宝友,等.2006.雷暴云内闪电双层、分枝结构的数值模拟[J].中国科学(D辑:地球科学),36(5):486-496.Tan Yongbo,Tao Shanchang,Zhu Baoyou,et al.2006.Numerical simulations of the bi-level and branched structure of intracloud lightning flashes[J].Science in China(Ser.D),49(6):661-672,doi:10.3969/j.issn.1674-7240.2006.05.011.
谭涌波,陶善昌,祝宝友,等.2007.云闪放电对云内电荷和电位分布影响的数值模拟[J].地球物理学报,50(4):1053-1065.Tan Yongbo,Tao Shanchang,Zhu Baoyou,et al.2007.A simulation of the effects of intra-cloud lightning discharges on the charges and electrostatic potential distributions in a thundercloud[J].Chinese Journal of Geophysics(in Chinese),50(4):1053-1065,doi:10.3321/j.issn:0001-5733.2007.04.012.
Wang C E.2005.A modeling study of the response of tropical deep convection to the increase of cloud condensation nuclei concentration:1.Dynamics and microphysics[J].J.Geophys.Res.,110(D21):D21211,doi:10.1029/2004JD005720.
Wang Y,Wan Q,Meng W,et al.2011.Long-term impacts of aerosols on precipitation and lightning over the Pearl River Delta megacity area in China[J].Atmospheric Chemistry and Physics,11(23):12421-12436,doi:10.5194/acp-11-12421-2011.
Westcott N E.1995.Summertime cloud-to-ground lightning activity around major Midwestern Urban areas[J].J.Appl.Meteor.,34(7):1633-1642,doi:10.1175/1520-0450-34.7.1633.
Williams E,Stanfill S.2002.The physical origin of the land-ocean contrast in lightning activity[J].Comptes Rendus Physique,3(10):1277-1292,doi:10.1016/S1631-0705(02)01407-X.
Yin Y,Levin Z,Reisin T G,et al.2000.The effects of giant cloud condensation nuclei on the development of precipitation in convective clouds-A numerical study[J].Atmospheric Research,53(1-3):91-116,doi:10.1016/S0169-8095(99)00046-0.
Zhao P G,Yin Y,Xiao H.2015.The effects of aerosol on development of thunderstorm electrification:A numerical study[J].Atmospheric Research,153:376-391,doi:10.1016/j.atmosres.2014.09.011.
赵鹏国,银燕,肖辉,等.2016.气溶胶对热带气旋强度及电过程影响的数值模拟研究[J].气象科学,36(1):1-9.Zhao Pengguo,Yin Yan,Xiao Hui,et al.2016.Numerical simulation of the effects of aerosol on the intensity and electrification of tropical cyclone[J].Journal of the Meteorological Sciences(in Chinese),36(1):1-9,doi:10.3969/2015jms.0012.
Ziegler C L,MacGorman D R,Dye J E,et al.1991.A model evaluation of noninductive graupel-ice charging in the early electrification of a mountain thunderstorm[J].J.Geophys.Res.,96(D7):12833-12855,doi:10.1029/91JD01246.
Cooper W A.1980.A method of detecting contact ice nuclei using filter samples[C]//Proceedings of the 8th International Conference on Cloud Physics.Clermont-Ferrand,France,665-668.
邓美玲,银燕,赵鹏国,等.2017.云凝结核浓度对雷暴云电过程影响的数值模拟研究[J].大气科学,41(1):106-120.Deng Meiling,Yin Yan,Zhao Pengguo,et al.2017.Effects of cloud condensation nuclei concentration on the electrification of thunderstorm:A numerical simulation[J].Chinese Journal of Atmospheric Sciences(in Chinese),41(1):106-120,doi:10.3878/j.issn.1006-9895.1608.15286.
Fan J W,Zhang R Y,Li G H,et al.2007.Simulations of cumulus clouds using a spectral microphysics cloud-resolving model[J].J.Geophys.Res.,112(D4):D04201,doi:10.1029/2006JD007688.
Fletcher N H.1962.Physics of Rain Clouds[M].London:Cambridge University Press,390pp.
Gardiner B,Lamb D,Pitter R L,et al.1985.Measurements of initial potential gradient and particle charges in a Montana summer thunderstorm[J].J.Geophys.Res.,90(D4):6079-6086,doi:10.1029/JD090iD04p06079.
Heymsfield A J,Miloshevich L M.1993.Homogeneous ice nucleation and supercooled liquid water in orographic wave clouds[J].J.Atmos.Sci.,50(15):2335-2353,doi:10.1175/1520-0469(1993)050<2335:HINASL>2.0.CO;2.
Heymsfield A J,Miloshevich L M,Schmitt C,et al.2005.Homogeneous ice nucleation in subtropical and tropical convection and its influence on cirrus anvil microphysics[J].J.Atmos.Sci.,62(1):41-64,doi:10.1175/JAS-3360.1.
Heymsfield A J,Sabin R M.1989.Cirrus crystal nucleation by homogeneous freezing of solution droplets[J].J.Atmos.Sci.,46(14):2252-2264,doi:10.1175/1520-0469(1989)046<2252:CCNBHF>2.0.CO;2.
胡志晋,何观芳.1987.积雨云微物理过程的数值模拟(一)微物理模式[J].气象学报,45(4):467-484.Hu Zhijin,He Guanfang.1987.Numerical simulation of microprocesses in cumulonimbus clouds(I)microphysical model[J].Acta Meteorologica Sinica(in Chinese),45(4):467-484,doi:10.11676/qxxb1987.060.
Kar S K,Liou Y A,Ha K J.2009.Aerosol effects on the enhancement of cloud-to-ground lightning over major urban areas of South Korea[J].Atmospheric Research,92(1):80-87,doi:10.1016/j.atmosres.2008.09.004.
Li G H,Wang Y,Zhang R Y.2008.Implementation of a two-moment bulk microphysics scheme to the WRF model to investigate aerosol-cloud interaction[J].J.Geophys.Res.,113(D15):D15211,doi:10.1029/2007JD009361.
Lyons W A,Uliasz M,Nelson T E.1998.Large peak current cloud-toground lightning flashes during the summer months in the contiguous United States[J].Mon.Wea.Rev.,126(8):2217-2233,doi:10.1175/1520-0493(1998)126<2217:LPCCTG>2.0.CO;2.
Mansell E R,MacGorman D R,Ziegler C L,et al.2002.Simulated three-dimensional branched lightning in a numerical thunderstorm model[J].J.Geophys.Res.,107(D9):4075,doi:10.1029/2000JD000244.
Mansell E R,MacGorman D R,Ziegler C L,et al.2005.Charge structure and lightning sensitivity in a simulated multicell thunderstorm[J].J.Geophys.Res.,110(D12):D12101,doi:10.1029/2004JD005287.
Mansell E R,Ziegler C L.2013.Aerosol effects on simulated storm electrification and precipitation in a two-moment bulk microphysics model[J].J.Atmos.Sci.,70(7):2032-2050,doi:10.1175/JAS-D-12-0264.1.
Mitzeva R,Latham J,Petrova S.2006.A comparative modeling study of the early electrical development of maritime and continental thunderstorms[J].Atmospheric Research,82(1-2):26-36,doi:10.1016/j.atmosres.2005.01.006.
Murray N D,Orville R E,Huffines G R.2000.Effect of pollution from Central American fires on cloud-to-ground lightning in May 1998[J].Geophys.Res.Lett.,27(15):2249-2252,doi:10.1029/2000GL011656.
Orville R E,Huffines G,Nielsen-Gammon J,et al.2001.Enhancement of cloud-to-ground lightning over Houston,Texas[J].Geophys.Res.Lett.,28 (13):2597-2600,doi:10.1029/2001GL012990.
Saunders C P R,Keith W D,Mitzeva R P.1991.The effect of liquid water on thunderstorm charging[J].J.Geophys.Res.,96(D6):11007-11017,doi:10.1029/91JD00970.
Shi Z,Tan Y B,Tang H Q,et al.2015.Aerosol effect on the land-ocean contrast in thunderstorm electrification and lightning frequency[J].Atmospheric Research,164-165:131-141,doi:10.1016/j.atmosres.2015.05.006.
师正,谭涌波,唐慧强,等.2015.气溶胶对雷暴云起电以及闪电发生率影响的数值模拟[J].大气科学,39(5):941-952.Shi Zheng,Tan Yongbo,Tang Huiqiang,et al.2015.A numerical study of aerosol effects on the electrification and flash rate of thunderstorms[J].Chinese Journal of Atmospheric Sciences(in Chinese),39(5):941-952,doi:10.3878/j.issn.1006-9895.1412.14230.
Steiger S M,Orville R E.2003.Cloud-to-ground lightning enhancement over Southern Louisiana[J].Geophys.Res.Lett.,30(19):1975,doi:10.1029/2003GL017923.
Sun A P,Chun H Y,Baik J J,et al.2002.Influence of electrification on microphysical and dynamical processes in a numerically simulated thunderstorm[J].J.Appl.Meteor.,41:1112-1127,doi:10.1175/1520-0450(2002)041<1112:IOEOMA>2.0.CO;2.
Takahashi T.1978.Riming electrification as a charge generation mechanism in thunderstorms[J].J.Atmos.Sci.,35(8):1536-1548,doi:10.1175/1520-0469(1978)035<1536:REAACG>2.0.CO;2.
谭涌波.2006.闪电放电与雷暴云电荷、电位分布相互关系的数值模似[D].中国科学技术大学博士学位论文,173pp.Tan Yongbo.2006.Numerical simulation of the relationship of the lightning discharge with the space charge and potential distribution in thundercloud[D].Ph.D.dissertation(in Chinese),University of Science and Technology of China,173pp.
Tan Y B,Peng L,Shi Z,et al.2016.Lightning flash density in relation to aerosol over Nanjing(China)[J].Atmospheric Research,174-175:1-8,doi:10.1016/j.atmosres.2016.01.009.
Tan Y B,Shi Z,Chen Z L,et al.2017.A numerical study of aerosol effects on electrification of thunderstorms[J].Journal of Atmospheric and SolarTerrestrial Physics,154:236-247,doi:10.1016/j.jastp.2015.11.006.
Tan Y B,Tao S C,Liang Z W,et al.2014.Numerical study on relationship between lightning types and distribution of space charge and electric potential[J].J.Geophys.Res.,119(2):1003-1014,doi:10.1002/2013JD019983.
谭涌波,马肖,向春燕,等.2017.气溶胶对雷暴云电过程影响的数值模拟研究[J].地球物理学报,60(8):3041-3050.Tan Yongbo,Ma Xiao,Xiang Chunyan,et al.2017.A numerical study of the effects of aerosol on electrification and lightning discharges during thunderstorms[J].ChineseJournal of Geophysics(in Chinese),60(8):3041-3050,doi:10.6038/cjg20170812.
谭涌波,陶善昌,祝宝友,等.2006.雷暴云内闪电双层、分枝结构的数值模拟[J].中国科学(D辑:地球科学),36(5):486-496.Tan Yongbo,Tao Shanchang,Zhu Baoyou,et al.2006.Numerical simulations of the bi-level and branched structure of intracloud lightning flashes[J].Science in China(Ser.D),49(6):661-672,doi:10.3969/j.issn.1674-7240.2006.05.011.
谭涌波,陶善昌,祝宝友,等.2007.云闪放电对云内电荷和电位分布影响的数值模拟[J].地球物理学报,50(4):1053-1065.Tan Yongbo,Tao Shanchang,Zhu Baoyou,et al.2007.A simulation of the effects of intra-cloud lightning discharges on the charges and electrostatic potential distributions in a thundercloud[J].Chinese Journal of Geophysics(in Chinese),50(4):1053-1065,doi:10.3321/j.issn:0001-5733.2007.04.012.
Wang C E.2005.A modeling study of the response of tropical deep convection to the increase of cloud condensation nuclei concentration:1.Dynamics and microphysics[J].J.Geophys.Res.,110(D21):D21211,doi:10.1029/2004JD005720.
Wang Y,Wan Q,Meng W,et al.2011.Long-term impacts of aerosols on precipitation and lightning over the Pearl River Delta megacity area in China[J].Atmospheric Chemistry and Physics,11(23):12421-12436,doi:10.5194/acp-11-12421-2011.
Westcott N E.1995.Summertime cloud-to-ground lightning activity around major Midwestern Urban areas[J].J.Appl.Meteor.,34(7):1633-1642,doi:10.1175/1520-0450-34.7.1633.
Williams E,Stanfill S.2002.The physical origin of the land-ocean contrast in lightning activity[J].Comptes Rendus Physique,3(10):1277-1292,doi:10.1016/S1631-0705(02)01407-X.
Yin Y,Levin Z,Reisin T G,et al.2000.The effects of giant cloud condensation nuclei on the development of precipitation in convective clouds-A numerical study[J].Atmospheric Research,53(1-3):91-116,doi:10.1016/S0169-8095(99)00046-0.
Zhao P G,Yin Y,Xiao H.2015.The effects of aerosol on development of thunderstorm electrification:A numerical study[J].Atmospheric Research,153:376-391,doi:10.1016/j.atmosres.2014.09.011.
赵鹏国,银燕,肖辉,等.2016.气溶胶对热带气旋强度及电过程影响的数值模拟研究[J].气象科学,36(1):1-9.Zhao Pengguo,Yin Yan,Xiao Hui,et al.2016.Numerical simulation of the effects of aerosol on the intensity and electrification of tropical cyclone[J].Journal of the Meteorological Sciences(in Chinese),36(1):1-9,doi:10.3969/2015jms.0012.
Ziegler C L,MacGorman D R,Dye J E,et al.1991.A model evaluation of noninductive graupel-ice charging in the early electrification of a mountain thunderstorm[J].J.Geophys.Res.,96(D7):12833-12855,doi:10.1029/91JD01246.